Mounting devices are used to attach objects to a tire, and particularly to an inner liner of a tire. One application is to attach a radio frequency identification (“RFID”) tag or chip to the inner liner of a tire. Another application is to secure a pressure or temperature-sensing device to the inner liner of the tire. Various fasteners are used to connect the object to the mounting device, including hook and loop fasteners, threaded connectors, clamps, pins, and snap-fit structures.